Place eggs into a saucepan and cover with cold water. Bring water to a boil, then immediately remove from the heat. Cover and let eggs stand in hot water for 10 to 12 minutes.
Remove eggs from hot water and run under cold running water to cool. Roll cooled eggs back and forth on the counter to crush the shells, then return to the cold water and soak for up to 1 hour. They will peel very easily then.
Place peeled eggs into a large bowl or large wide-mouthed jar with a lid. Pour in pickled beets and juice, then add onions. Cover and refrigerate for at least 24 hours, or up to 2 days for best results. Turn the jar or stir once or twice to be sure the eggs are evenly colored.
Slice eggs in half and arrange on a tray to serve.